1 Answer
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If you are looking for a formula for $\epsilon_0$ (vacuum permittivity), you will not find it, because $\epsilon_0$ is a constant.
$$\epsilon_0=8.854187817\times 10^{−12} \frac{F}{m}$$
In other hand, permitivity $\epsilon$ is defined as follows
$$\epsilon=(1+\chi_e)\epsilon_0$$
Where $\chi_e$ is called the electric susceptibility, and is defined with
$$\mathbf{P}=\chi_{e}\epsilon_{0}\mathbf{E}$$
Where $\mathbf{P}$ is the polarization vector.